Question

In the given figure, a square $OABC$ has been inscribed in the quadrant $OPBQ$. If $OA=20cm$ then the area of the shaded region is $[take\pi =3.14]$

• A. $214c{m}^2$
• B. $228c{m}^2$
• C. $222c{m}^2$
• D. $242c{m}^2$

Answer 1

The correct option is B $228c{m}^2$

Area of shaded region $=Areaof\left[OPBQ\right]-Areaof\left[OABC\right]$

$=\frac{1}{4}\pi r^2-a^2$

$[\because OA=a=20cmr=OB=OA\sqrt{2}=20\sqrt{2}cm]$

$=\frac{1}{4}\pi {\left(20\sqrt{2}\right)}^2-{20}^2$

$=200\pi -400=228{cm}^2$